• Title, Summary, Keyword: Relative Nodal Displacement

### A Relative Nodal Displacement Method for Element Nonlinear Analysis (상대 절점 변위를 이용한 비선형 유한 요소 해석법)

• Kim Wan Goo;Bae Dae sung
• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.4
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• pp.534-539
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• 2005
• Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian furmulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacement sand traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large deformations are analyzed to demonstrate the efficiency and validity of the proposed method.

### A Relative for Finite Element Nonlinear Structural Analysis (상대절점좌표를 이용한 비선형 유한요소해석법)

• Kang, Ki-Rang;Cho, Heui-Je;Bae, Dae-Sung
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.788-791
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• 2005
• Nodal displacements are referred to the Initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian formulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid fer structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One closed loop structure undergoing large deformations is analyzed to demonstrate the efficiency and validity of the proposed method.

### Multilevel Editing for Hierarchical B-spline Curves using Rotation Minimizing Frames (RMF을 이용한 계층적 B-spline 곡선의 다단계 편집기법)

• Zhang, Ci;Yoon, Seung-Hyun;Lee, Ji-Eun
• Journal of The Korea Computer Graphics Society
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• v.16 no.4
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• pp.41-50
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• 2010
• We present a new technique for multilevel editing of hierarchical B-spline curves. At each level, control points of a displacement function are expressed in the rotation minimizing frames (RMFs) [1] which are computed on nodal points of the curve at previous level. When the curve is edited at previous level, the corresponding RMFs are updated and the control points of the displacement function at current level are applied to the new RMFs, which maintains the relative details of the curve at current level to those of previous level. We demonstrate the effectiveness and robustness of the proposed technique using several experimental results.

### EFFICIENT COMPUTATION OF THE ACCELERATION OF THE CONTACT POINT BETWEEN ROTATING SURFACES AND APPLICATION TO CAM-FOLLOWER MECHANISM

• LEE K.
• International Journal of Automotive Technology
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• v.7 no.1
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• pp.115-120
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• 2006
• On a rotating contact surface of arbitrary shape, the relative velocity of the contact point sliding between the surfaces is computed with the basic geometries of the rotating surfaces, and the acceleration of the contact point between the contact surfaces is computed by using the relative velocity of the contact point. Thus the equation for the acceleration constraint between the contact surfaces in muitibody dynamics is not coupled with the parameters such as the relative velocity of the contact point. In case of the kinematic analysis, the acceleration of the contact point on any specific instant may also be efficiently computed by the present technique because the whole displacement of a full cycle need not be interpolated. Employing a cam-follower mechanism as a verification model, the acceleration of the contact point computed by the present technique is compared with that computed by differentiating the displacement interpolated with a large number of nodal points.